Re: [Audacity-devel] Classic Filters status

[Steve t. F. <ste...@gm...>]

On 2 January 2015 at 19:24, Federico Miyara <fm...@fc...> wrote:
>
> Steve,
>
> That makes sense where component count, physical size and
> manufacturing costs of analog filters are relevant, but surely it is a
> spurious trade off for digital filters. Yes a 2nd order Chebyshev
> filter may have a slightly steeper roll-off compared with a second
> order Butterworth, (at the expense of ripple in either the pass band
> or stop band), but for digital filters there is absolutely no need for
> that compromise - if you want a steeper roll-off, use a higher order
> Butterworth filter and then you get a steeper roll-off with no ripple.
>
>
> Higher order in Butterworth means more phase distortion (as in any analog
> filter), what in turn means worse transient response (for instance, more
> ringing. It ios true that for the same order Chebyshev is worse than
> Butterworth, but a Butterworth of larger order has worse transient behavior,

Sorry but that is just not true, but it does demonstrate the point
that including Chebyshev filters makes the effect too complicated and
confusing for the vast majority of users (including many very
experienced users).

Buterworth filters have a more linear phase response in the pass band
than either type I or type II Chebyshev filters. A type 1 Chebyshev
low pass filter will ring more at frequencies a little below the
corner frequency than a Butterworth filter, and a type 1 Chebyshev
high pass will ring more at frequencies a little above the corner
frequency than a Butterworth filter.

Type 2 Chebyshev filters ring less near the corner frequency, but at
the expense of significantly worse roll-off characteristics and
stop-band performance.

Stephen Butterworth owes his immortal fame to finding the sweet spot
between type I and type II, where an IIR filter of a given order most
closely resembles the ideal high/low pass.
http://en.wikipedia.org/wiki/Butterworth_filter

Attached is a screen shot demonstrating the ringing effect of a 4th
order Butterworth high pass filter compared with 3rd order Chebyshev
type I and type II filters on a 2 ms noise pulse (Waveform (dB) view).

Steve

>
> Regards,
>
> Federico
>
>
>
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